Generalized Heisenberg-Euler formula in Abelian gauge theory with parity violation

Abstract

A generalized Heisenberg-Euler formula is given for an Abelian gauge theory having vector as well as axial vector couplings to a massive fermion. So, the formula is applicable to a parity-violating theory. The gauge group is chosen to be $U(1)$. The formula is quite similar to that in quantum electrodynamics, but there is a complexity in which one factor (related to spin) is expressed in terms of the expectation value. The expectation value is evaluated by the contraction with the one-dimensional propagator in a given background field. The formula affords a basis to the vacuum magnetic birefringence experiment, which aims to probe the dark sector, where the interactions of the light fermions with the gauge fields are not necessarily parity conserving.

arXiv comment36 pages, 4 figures. A comment added in Conclusion and discussion, matches the published version

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Cited by in corpus (6)

• Probing CP Violation in Photon Self-Interactions with Cavities
• Gravity Analog Model of Non-equilibrium Thermodynamics
• Euler-Heisenberg Lagrangian under an axial gauge field
• Impossibility of obtaining a CP-violating Euler-Heisenberg effective theory from a viable modification of QED
• Vacuum Magnetic Birefringence Experiment as a probe of Dark Sector
• Induced CP-violation in the Euler-Heisenberg Lagrangian